A flurry of banking news this week will illustrate the contrasting fortunes of the two bailed-out banks, Lloyds Banking Group and Royal Bank of Scotland, and determine whether Barclays intends to raise up to £7bn of fresh capital.

The scene will be set for a sale of the taxpayer's 39% stake in Lloyds when the bank reports six-monthly profits on 1 August. By contrast, RBS will concede on 2 August that it faces more time in government ownership as it prepares to name a chief executive to replace the departing Stephen Hester.

Before then, on 30 July, Barclays will reveal the outcome of its tussle with the City regulator over whether it needs to raise more capital – as much as £7bn according to some analysts – to meet a crucial risk test.

Speculation was mounting this weekend that Barclays could be considering raising new capital at a time when the stakes are high not just for bank bosses but also for officials at the Bank of England's new regulatory arm, the Prudential Regulation Authority (PRA), and for George Osborne, as he prepares for a Lloyds sell-off.

And while Antony Jenkins, who is close to completing his first year as Barclays chief executive, may want to find a way to meet the regulator's measure of risk – known as the leverage ratio – without tapping investors, he may resign himself to raising fresh funds. Jenkins has already discussed issuing bonds known as contingent convertible capital or "cocos".

His counterpart at Lloyds, António Horta-Osório, will be keen to present half-year numbers that show some semblance of normality after huge write-offs caused by bad property loans granted before the 2008 bailout and the £5bn cost of compensating customers mis-sold payment protection insurance.

For Hester, the half-year figures will be the last interims he presents at RBS, after being forced out by Osborne to clear the way for a new face at the helm of the 81%-taxpayer-owned bank. Amid speculation that his replacement could be named this week, analysts believe an internal promotion would provide the quickest and easiest solution.

"We continue to believe that an internal appointment remains the most likely outcome, with Ross McEwan, head of retail, and Chris Sullivan, head of corporate, the likely candidates," said John-Paul Crutchley, a banks analyst at UBS.

The new RBS chief executive will take over a lender in the throes of a review that could lead to a carve-out of a "bad bank" saddled with up to £105bn of toxic loans, and fresh speculation about the future of its investment bank. Osborne has admitted this review will delay any immediate sell-off of the taxpayer's 81% holding, but the same is not true of Lloyds, where the sale of at least 10% of the stake is thought imminent.

"Setting out a strategy or timetable for resuming dividend payments would help support the anticipated sell-down of UK government shares," said Crutchley.

He made the contrast with Barclays, which began paying a nominal 1p-a-quarter dividend in 2009, after a 15-month pause caused by the banking crisis, despite having a lower capital position than Lloyds and also failing a capital test set by the PRA last month.

The PRA's new emphasis on a 3% leverage ratio – a test failed by both Barclays and Nationwide building society – has led to weeks of speculation about whether Barclays will need to raise fresh funds, and threats from Jenkins to cut back on lending.

But after Nationwide secured an agreement to achieve the ratio by the end of 2015 – a deadline that Barclays had already been aiming for – some thought a fundraising could be avoided. Gary Greenwood, banks analyst at Shore Capital, pointed out that giving Barclays a different deadline may appear unfair, but it seems likely that the PRA will demand the bank reach the ratio before the end of 2014. If the PRA set the end of 2013 as a deadline, Greenwood said, Barclays would need to raise almost £7bn of capital or shrink its balance sheet by 15% – some £230bn.

Ian Gordon, banks analyst at Investec, wonders whether Barclays might raise some capital anyway, even if the PRA deadline were more lenient, although he thinks such a move would be unnecessary.

This now appears to be under consideration: but Osborne, for one, will be most focused on the share price of Lloyds. Its stock market value has recently eclipsed Barclays' in the flurry of speculation that a sell-off of the government stake will begin as soon as possible after the results are published on Thursday.